II$.$ Clustering $(10$ pts$)$

Assume the following dataset is given:

$(2,5),(3,4),(7,3),(4,4),(9,8),(1,2),(3,0),(5,6),(7,8),(1,1)$

K $-$Means is run with $k=3$ to cluster the dataset. Moreover, Manhattan distance is used as the distance function to compute distances between centroids and objects in the dataset.

K$-$Mean's initial centroids C$1,$ C$2,$ and C$3$ are as follows:

Cl: $(2,0)$

I

C$.(5,3)$

C$3$: $(8,7)$

Now K$-$means is run for a single iteration.

a$.$ Assign each data point to one of the three centrold based on $k-$means algorithm. $(5$ pts$)$

Cluster $1-$C$1$:

Cluster $2-$C$2$:

Cluster $3-$C$3$:

b$.$ Based on the above result, re$-$calculate the new centrold for each cluster $($you can use fraction for your results$).(5$ pts$)$

New Centroid for cluster $1$:

New Centroid for cluster $2$:

New Centroid for cluster $3$;